Trading Option Butterfly Strategies
Butterflies fit into the class of “non-directional” strategies. In terms of market opinion they are similar to straddles and strangles in that one is not primarily guessing a particular direction in the market, but rather the size of that movement.
• Long butterflies should be used when one is predicting little or no directional movement or a “trading range” in the underlying, and the trader seeks to profit from an increase in the value of the position due to time decay or falling implied volatility.
• Short butterflies should be used when one is predicting a large magnitude move in either direction, and the trader pursues profit from a decrease in the value of the overall position due to an increase in implied volatility or a move away from your long strikes.
Butterfly Spread Explained
The classic long butterfly consists of two longs and two shorts. Typically a long at one strike, two shorts at a strike greater than the long and then another long at a strike greater yet than your short strike. These three strikes are usually equidistant from each other and they are usually all calls or all puts in the same expiry (of course on the same underlying).
Example: Long Butterfly
IBM January 95 calls +1
IBM January 100 calls -2
IBM January 105 calls +1
This gives you, a long vertical spread and a short vertical spread.
Depending whether you sold the middle strike (the body) or sold the lowest and highest strikes (the wings), determines whether you are long the butterfly or short it. Whatever you do with the wings is what you have done with the spread. Long butterfly spreads are safer when you construct them with a lot of time left until expiry (they are usually very inexpensive) and get more expensive as one gets closer to expiry with the spread still near the money.
Since you are selling the center and buying wings, you have a chance of making a maximum of the difference between the two strikes, less your cost of the butterfly.
The most you can lose is the amount you paid for the butterfly, giving most typical butterflies a 5:1 up to a 10:1 risk/reward ratio. Expanding out to skip a strike and do butterflies with a larger span, to say 10-point butterflies, increases the cost, but also increases the range of payout and the risk/reward stays high.
I want you to think of these now, because they are a safer way to sell premium than just selling premium naked. As the volatilities climb, butterfly spreads should get “cheaper” and this is a fine time to put
some elongated butterflies or butterflies that skip strikes in the middle (called Condors) on in the May through August expirations.
The Long Butterfly
Think of a long butterfly as containing an embedded short straddle wrapped within a synthetic long strangle. This type of structure allows the properly positioned long butterfly to capitalize from time decay and/or falling implied volatility just as a short straddle would. The big difference is that the long strangle “wrap” of the long butterfly severely limits the risk in the position, making it an appealing “directionless” strategy for risk-adjusted return traders.
Butterflies are ideally suited for trading in directionless markets: The foundational reason to put on a butterfly is to target a well-defined price range within which the stock will trade at expiration.
This statement begs the question, “What is a directionless market?” A directionless, or “sideways” market is one that shows no definite or sustained direction in price movement. Although the price of the underlying may fluctuate, it tends to trade within a certain well-defined range, i.e. it doesn’t penetrate either the defined support level or the defined resistance level.
It should be noted that directionless markets are the most common markets a trader encounters; more so than either a bull or a bear market! The adept trader will develop the ability to identify such a market by recognizing when a stock is consolidating. An adept studying of charts (technical analysis) is important here
Why do we say that the long Butterfly is a “limited risk” strategy? That’s simple: if you put on a long Butterfly, you can never lose more than the initial debit paid out. The Butterfly is constituted so that it is “exposed” to losses on either side of its “body”, but this exposure is hedged by the location of the “wings”.
Why do we say that the Butterfly is a “limited reward” strategy? Well, at expiration the long Butterfly will always have a value between zero and the width between each strike price (5 points here). In other words, the price of a 5-point Butterfly will never exceed $5.
Note that the spread will be worth its maximum value if it closes right at the strike of the shorts. If this happens, the long OTM (out of the money) option as well as the two shorts will expire worthless. The long ITM (in the money) option, however, will expire worth its full value of $5. So we know that the greater the chance of it closing at the middle strike on expiration, the more expensive it will be.
Any movement away from the middle strike will cause the spread to lose value. The worst-case scenario occurs if it closes either below the lowest strike long option, or above the highest strike long option. In our example above, the call Butterfly will lose value below $100, because as stock drops below $100 the ITM 95 call will begin to lose value. The call Butterfly loses value above $105 because the loss from the two short 100 calls will be twice as much as the gain from the 95 call.
Greek Values and the Butterfly
The price of the butterfly spread becomes increasingly more sensitive to changes in the underlying with thirty days or less to go until expiration. The greeks of the butterfly respond the same way, in that they can also change dramatically and exponentially with less time to expiration.
But for all of the greek values, keep in mind that the delta, gamma, theta, or vega is not of much interest if the contracts in the spread are ninety days or more away from expiration. Far away from expiration, the greek values are minor factors; they become noteworthy only when the contracts are within thirty days of expiring.
Option Butterfly Spreads & Delta
For a long butterfly, such as the $150/$155/$160 spread in the example, the delta will be as follows:
• Positive when the underlying share price falls below the inside strike price ($155)
• Neutral when it matches the inside strike price
• Negative when it climbs above the inside strike price
The butterfly reaches its greatest value when the price of the underlying equals the inside strike price. Therefore, if the share price falls below the middle strike, that share price must rise for the butterfly to make money—hence the positive deltas. If the price of the underlying asset is above the middle strike price, it must fall for the butterfly to make money. That leads to a negative delta value.
Option Butterfly Spreads & Gamma
The gamma value of a long butterfly flows from positive to negative, or vice versa. When the underlying price reaches the outer strike prices of the butterfly, the gamma is positive. This shows that the butterfly would produce positive deltas if the underlying share price rises, and negative deltas if that share price falls, albeit to the extent that the underlying is close to a long strike. This matches the behavior of the delta of the long butterfly as shown in Figure 9.
Meanwhile, the gamma of the long butterfly is negative when the underlying share price matches the inside strike price (see Figure 9). This shows that the butterfly will create negative deltas if the underlying share price rises and positive deltas if the share price falls. But you want your delta to be neutral; you want the share price to match the inside strike price and stay there.
Option Butterfly Spreads & Theta
Think of theta as the opposite of gamma. If a long butterfly is negative gamma, the theta will be positive; if a short butterfly is positive gamma, it will have a negative theta. For any butterfly, the theta will be positive if the stock price approaches the inside strike price.
As the expiration date approaches, a positive theta is good for a long butterfly and bad for a short butterfly. If, however, the underlying price trades either high or low, and thus near one of the outer strike prices, the theta is positive for a short butterfly and negative for a long butterfly (see Figure 10).
That is, if the underlying price is close to one of the outer strike prices, it benefits the holder of the short butterfly, because the theta will be positive, but the theta will be negative for the long butterfly. With the short butterfly, remember, you sold the contracts with the outside strike prices (say, $60 and $50), bought two contracts with inside strike prices ($55 each), and earned a net premium in the transaction.
With a short butterfly, you make a profit if the share prices climb toward the highest strike price ($60) or fall toward the lowest strike price ($50). The short butterfly profits if the market is active, and the theta tends to reflect that.
This is an excerpt from Managing Expectations by Tony Saliba.
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